The expression curl $$\left( {grad\,f} \right)$$ where $$f$$ is a scalar function is

The particular solution for the differential equation $${{{d^2}y} \over {d{t^2}}} + 3{{dy} \over {dx}} + 2y = 5\cos x$$ is

The one dimensional heat conduction partial difference equation $$\,\,{{\partial T} \over {\partial t}} = {{{\partial ^2}T} \over {\partial {x^2}}}\,\,$$ is

$${i^i}$$, where $$i\, = \,\sqrt { - 1} $$ is given by